On your scale, I'd put programming somewhere around Aleph0.
Programming is completely equivalent to constructive Maths (see http://en.wikipedia.org/wiki/Constructivism_(mathematics) ). Constructive Maths is basically regular (classical) Maths, with the acknowlegement that the halting problem is undecidable. One major consequence of this is that we can't use the Law of the Excluded Middle (ie. "for all P, P or not P").
There's some really interesting research going on here that's far outstrips 'advanced calculus', for example take a look at Homotopy Type Theory.
Programming is completely equivalent to constructive Maths (see http://en.wikipedia.org/wiki/Constructivism_(mathematics) ). Constructive Maths is basically regular (classical) Maths, with the acknowlegement that the halting problem is undecidable. One major consequence of this is that we can't use the Law of the Excluded Middle (ie. "for all P, P or not P").
There's some really interesting research going on here that's far outstrips 'advanced calculus', for example take a look at Homotopy Type Theory.